Скачать или смотреть Class 9th maths Ex.6.2 Q3 II Lines and Angles II Ch -6 , Ncert solutins II Cbse standard maths

Class 9th maths Ex.6.2 Q3 II Lines and Angles II Ch -6 , Ncert solutins II Cbse standard maths, honours maths for cbse students class9th standard maths II
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Here are *Class 9 – Chapter: Lines and Angles* complete notes in simple and students




🧠 *Chapter: Lines and Angles – Complete Notes*

✅ *1. Basic Terms*

| Term | Meaning |
| ---------------- | ------------------------------------------------------------------------------------ |
| *Point* | It shows an exact position. |
| *Line* | A straight path that extends endlessly in both directions. |
| *Line Segment* | A part of a line with two fixed endpoints. |
| *Ray* | A part of a line that has one fixed endpoint and extends endlessly in one direction. |
| *Plane* | A flat surface that extends in all directions. Types of Angles**

| Angle Type | Measure | Diagram Idea |
| ------------------ | --------------------- | ------------ |
Acute Angle* | Less than 90° | |
Right Angle** | Exactly 90° | |
Obtuse Angle** Straight Angle** | Exactly 180° | |
| *Reflex Angle* | Between 180° and 360° | |
| *Complete Angle* | 360° | |

of Pairs of Angles**

| Angle Pair | Definition | Key Point |
| ------------------------------ | ---------------------------------------------------------- | --------------------------- |
| *Adjacent Angles* | Share a common arm and a common vertex, but do not overlap | Side-by-side angles |
| *Linear Pair* | Adjacent angles whose sum is 180° | Forms a straight line |
| *Vertically Opposite Angles* | Formed when two lines intersect | They are equal |
| *Complementary Angles* | Sum = 90° | Can be separate or adjacent |
| *Supplementary Angles* | Sum = 180° | Can be separate or adjacent
Lines and Their Relationships**
| Term | M |
| ---------------------- | ------------------------------------------------------------ |
| *Parallel Lines* | Lines that never meet and are always the same distance apart |
| *Intersecting Lines* | Lines that meet at one point |
| *Transversal* | A line that inters
| Angles | Position | Rule |
| ---------------------------------------------- | ------------------------------------------ | -------------------------------- |
| *Corresponding Angles* | Same relative position | Equal if lines are parallel |
| *Alternate Interior Angles* | Inside opposite sides of the transversal | Equal if lines are parallel |
| *Alternate Exterior Angles* | Outside opposite sides of the transversal | Equal if lines are parallel |
| *Interior Angles on Same Side* (Co-Interior) | Inside and on the same side of transversal | Sum = 180° if lines are parallel |
| *Exterior Angles on Same Side* | Outside and same side | S° if lines are parallel Important Theorems/Properties**
1. *Linear Pair Axiom*
→ If a ray stands on a line, it forms a linear pair of angles whose sum is 180°.

2. *Vertically Opposite Angles Theorem*
→ Vertically opposite angles are equal.

3. Parallel Line Theorem**
→ If a transversal intersects two parallel lines, the following pairs are equal:

Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
And:
Co-Interior Angles are supplementary (sum = 180°
Ang Sum Property of a Triangle**

The sum of all interior angles of a triangle = *180°*
( ∠A + ∠B + ∠C = 180° )
Angle Property

Exterior angle of a triangle = sum of the *two interior opposite angles*
( Exterior ∠ = ∠Interior\ opposite1 + ∠Interior\ opposite2 ) Extra Concepts for Class 9**

| Term | Meaning |
| -------------------------- | --------------------------------------- |
| *Perpendicular Lines* | Two lines that meet at 90° |
| *Transversal Angle Test* | Used to check if two lines are parallel |
| *Collinear Points* | Points on the same line |